Cross-axis acceleration compensation for angular rate sensing apparatus

ABSTRACT

A low-cost, two-axis rate and acceleration sensor utilizing piezoelectric generator elements affixed to the rotating housing of an inside-out synchronous motor. Signals generated by the piezoelectric bender elements are amplified, compensated, balanced, and converted to FM signals for transmission off the rotating assembly.

BACKGROUND OF THE INVENTION

This invention relates generally to reference apparatus for navigablevehicles such as aircraft, and more particularly, to rate/accelerationsensors used in an attitude and heading reference system. Advancement inthe art of precision flight control and guidance apparatus for aircraft,missiles, and space vehicles depends in part on progress in sensortechnology. Present computer technology allows sophisticated and complexsignal processing at reasonable cost, but the information processed isfrequently derived from sensors having a cost which is adisproportionate part of the system cost.

A reference system having inertial instruments rigidly fixed along avehicle-based orientation reference wherein the instruments aresubjected to vehicle rotations and the instrument outputs are stabilizedcomputationally istead of mechanically is termed a gimballess orstrapped-down system. Such systems generally include computing meansreceiving navaid data such as magnetic and radio heading; air data suchas barometric pressure, density, and air speed; along with outputsignals of the inertial instruments for generating signalsrepresentative of vehicle position and orientation relative to a systemof coordinate axes, usually earth oriented. The presence of high angularrates assocaited with strapped-down systems adversely affectsperformance and mechanization requirements. Consequently, such referencesystems have been used extensively in missiles, space, and militaryvehicles, but their use in commerical aircraft has been less extensivebecause of economic constraints associated with the manufacture ofprecision mechanical assemblies, i.e., gyroscopes and other precisionsensors. Strapped-down inertial reference systems become practical forcommercial aircraft from the standpoint of cost of ownership, weight,reliability, and maintainability with the advent of small, lightweight,highly accurate and relatively low-cost rate sensors and accelerometers.Angular rate sensing apparatus utilizing rotating piezoelectricgenerators are known; see for example U.S. Pat. Nos. 2,716,893 and4,197,737. Such devices generally comprise piezoelectric generatorelements mounted to a rotatable drive shaft and oriented for generatingsignals responsive to particular bending forces sensed by theinstrument; the processing of signals derived form such instrumentationinvolves the measurement, amplification and transmission of very lowlevel DC and low frequency signals. Prior art devices have exhibitedsignal degradations which make the devices unsuitable for someapplications. For example, the signals being processed may containundesirable carrier harmonics, DC bias, and other noise components, suchas those caused by signal phase shifts and mechanical misalignments inthe system, which undesirable components must be rejected to preventdegradation of the low-level signals of primary interest.

In view of the problems of present state-of-the-art sensors, describedabove, it is a general objective of the present invention to develop animproved low-cost sensor for generating signals representative ofvehicle accelerations and angular rates.

A more specific object of the invention is to provide an improved sensorfor measuring angular rate about two axes and having relatively simplemechanical construction, low bias drift, and high sensitivity.

It is another object of the present inventon to provide an improvedangular rate sensor wherein signals resulting from undesiredacceleration sensitivity due to mechanical misalignment and externallyapplied vibrations are virtually eliminated.

SUMMARY OF THE INVENTION

In accordance with one aspect of the invention, there is provided animproved, low cost and compact sensor assembly which utilizes apiezoelectric generator bender element mounted exteriorly on a rotatingelement for sensing coriolis accelerations developed when the spin axisof the sensor assembly is rotated in space. Circuits mounted on therotating element amplify and convert the low-level DC signals generatedby the bender element for coupling off the rotating element. Undesiredsignals representative of cross-axis accelerations sensed by the benderelement are compensated for by adding two additional accelerometersangularly displaced from each other which sense accelerations in a planeperpendicular to the spin axis; a signal representative of a cancellingvector equal and opposite to the cross-axis acceleration signal isformed by selectively applying signal components of predeterminedamplitude and polarity of the output signals generated by the additionalaccelerometers to a summing junction along with the signal generated bythe bender element.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is pointed out with particularlity in the appended claims;however, specific objects, features, and advantages of the inventionwill bcome more apparent and the invention will best be understood byreferring to the following description of the preferred embodiment inconjunction with the accompanying drawings, in which:

FIG. 1 is a pictorial view, partially cut away, of a sensor assembly inaccordance with the present invention.

FIG. 2 is a section view of a sensor assembly in accordance with theinstant invention.

FIG. 3 is a pictorial view of a piezoelectric bender element utilized inthe practice of the invention.

FIG. 4 is a schematic block diagram of the sensor assembly includingcircuit elements, both on and off the rotating structure, associatedtherewith.

FIG. 5 is a diagramatic representation of linear acceleration sensorsuseful in explaining the operation of the present invention.

FIGS. 6A and 6B are diagramatic representations of angular rate andlinear acceleration sensors useful in explaining the operation of thepresent invention.

FIG. 6C is a vector diagram useful in explaining the operation of thepresent invention.

FIG. 6D is a simplified blocx diagram of one embodiment of compensationmeans utilized in the present invention.

FIG. 7 is a detailed electrical schematic diagram of the sensor assemblyof the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to the various views of the drawing for a more detaileddescription of the components, materials, construction, operation andother features of the invention by characters of reference, FIGS. 1 and2 show a sensor assembly 10 constructed in accordance with the presentinvention. The sensor assembly 10 comprises a hysteresis motor 12 havinga fixed axial shaft 14. The shaft 14 is mounted and rigidly affixed, ateither end thereof, to a structural member 16, 16¹ having an orientationfixed with respect to a vehicle (not shown) in which the sensor assembly10 is installed. A rotating element of the motor 12 comprises acylindrical motor housing or sleeve 18 journaled for rotation about theshaft 14 on bearings 20, 22, the spin axis 23 of the sleeve 18 beingcoaxial with the shaft 14. The bearings 20, 22 are endcap rollerbearings bonded with a preload to the shaft 14 and pressed into the endsof the motor housing 18. A stator 24 and its associated windings 26surrounds the shaft 14 and is affixed thereto. Leads 28 for supplyingalternating current to the stator windings 26 emanate from the motor viaa central bore 30 in the shaft 14. A cylindroid hysteresis ring 32 ofmagnetic material is mounted interiorly of the motor housing 18 forrotation therewith between a pair of ring spacers 34, 34¹. The spacers34, 34¹ are made from a non-magnetic material such as austeniticstainless steel, the preferred material being 304 stainless steel. Thehystersis ring 32 is juxtaposed with the stator 24, driving the rotatingelement in response to alternating current applied to the leads 28 ofthe stator windings 26. The motor housing 18 is made from martensiticstainless steel such as 416 stainless steel. The materials were chosento keep the bearing thermal expansion loop matched with respect tocoefficient of expansion so as to maintain the bearing preload overtemperature extremes. A motor such as the motor 12 having a fixed shaftand stator, and an externally disposed rotating structure, is termed aninside-out motor.

A pair of piezoelectric (PE) crystal assemblies 36, 38 are mountedexteriorly on the rotating motor housing 18 on opposide sides thereof.Each of the crystal assemblies 36, 38 comprises a base 50 to which apiezoelectric bender element 42 is mounted in cantilever fashion. Acover 44 in cooperation with the base 40 extended encloses the benderelement 42. Leads 46 conduct output signals generated by thepiezoelectric bender elements 42 via feedthrough terminals 48 toelectronic circuits carried on the rotating element of the sensorassembly 10. The piezoelectric bender element 42 of thepresently-described embodiment is the same as decribed in my co-pendingU.S. patent application Ser. No. 276,112, now U.S. Pat. No. 4,443,729,entitled Piezoelectric Sensor assigned to the same assignee as thepresent invention, which application is incorporated herein byreference.

Referring still to FIG. 1, a second pair of piezoelectric crystalassemblies 50, 52 are shown mounted exteriorly on the rotating motorhousing 18 for measuring accelerations in a plane perpendicular to thespin axis 23 of the sensor assembly 10. The crystal assemblies 50, 52are mounted having bending axes thereof essentially parallel with thespin axis 23 of the sensor assembly 10, and axes of sensitivityessentially perpendicular to the spin axis 23. "Essentially parallel"and "essentially perpendicular" mean as parallel and as perpendicular asmanufacture will reasonably allow, but including some slightmisalignment which may be detected in output signals generated by thecrystal assemblies. While the crystal assemblies 50, 52, are shownmounted orthogonally of each other, they can be mounted with their axesof sensitivity displaced with respect to each other by any angle, or onecould be omitted; however, a nominal 90° separation between two crystalassemblies is the preferred arrangement for reasons which will beexplained hereinafter.

A pair of annular circuit boards 54, 56 are mounted exteriorly of themotor housing 18 for rotation therewith by any suitable means such ascollars 58, 58¹. A cylindrical plate 59 (see FIG. 2) extending betweenthe peripheral ends of the circuit boards 54, 56 encloses the spacetherebetween, serving as a dust cover for the circuit devices carried onthe boards. The enclosure formed by the circuit boards 54, 56 and theplate 59 protects the PE crystal assemblies 36, 38, 50, 52 fromturbulent air currents which could be generated if the rotatingcomponents were not so protected. Referring to FIG. 2, an annular,air-gap power transformer having a stationary primary coil 60 affixed tothe shaft 14, and a rotating secondary coil 62 concentric with theprimary coil 60 and mounted inside the rotating sleeve 18 supplies powerto electronic circuits on the circuit boards 54, 56. Power leads 64transmitting alternating current are routed through the central bore 30of the shaft 14 and connected to the primary coil 60 of the powertransformer. Similarly, power leads 66 from the secondary coil 62 of thetransformer are routed via a slot 67 in the motor housing 18 to thecircuit boards 54, 56. An annular, air-core signal transformer having aprimary coil 68 mounted inside the sleeve 18 for rotation therewith anda secondary coil 70 affixed to the shaft 14 couples output signals ofcircuits (components of which are shown in FIG. 1) on circuit boards 54,56 via leads 72 routed through a slot 73 in the sleeve 18 to the primarycoil 68, and from the secondary coil 70 via leads 74 routed through acentral bore 75 of the shaft 14 to user circuits external of the sensorassembly 10.

Referring now to FIG. 3, there is shown in greater detail apiezoelectric bender element 78 like the bender elements 42 of FIG. 2.The bender element 78 comprises a cantilevered piezoelectric-crystalsensor 80 affixed to a mounting member or base 82. The bender element 78generates a voltage V_(o) on output leads 83, 84 which is proportionalto the bending moment generated by accelerations acting on the mass ofthe sensor 80 itself along an axis of sensitivity illustrated by theline 85, the bending axis of the bender element 78 being in the plane ofthe sensor 80 and parallel with the longitudinal dimension of the base82. The bender element 78 is inherently sensitive without the additionof proof mass. Additional details relating to construction and operationof the bender element 78 may be found in the aforementioned co-pendingapplication Ser. No. 276,112.

Referring to FIG. 1, the desired accelerations are available when thepiezoelectric bender elements 36, 38, 50, 52 are rotated at a fixedfrequency, 3120 revolutions per minute in the presently describedembodiment, about the spin axis 23 as shown in FIG. 1.

A measurement of linear acceleration is accomplished simply by measuringthe phase and amplitude of the AC signal obtained by rotating the benderelements 50, 52 in the plane of interest. For rate measurement, thepiezoelectric bender elements 36, 38 are oriented as shown in FIGS. 1and 2 to sense acceleration along the spin axis 23. The bender elements36, 38 are rotated at the fixed spin frequency, N, in radians persecond, the spin axis 23 being oriented and fixed, for example, alongthe roll axis of an aircraft, and the sensor assembly 10 measures pitchand yaw rate. As the aircraft experiences an angular rate perpendicularto the spin axis, a useful coriolis acceleration along the spin axisacts on the mass of the bender elements 36, 38. At a point (r, α) on thebender element, the acceleration along the spin axis is given by

    a=2Nrθcos(Nt-α)+2Nr ψsin(Nt-α)       (1)

where θ and ψ are pitch and yaw rates, r is the radial distance from thespin axis to the point on the bender element and α is the angularlocation of the point on the bender element from the axis about whichangular rate is being sensed. A sinusoidal output voltage V_(o) isgenerated by the bender element as a result of the force and stressexerted on the piezoceramic material therein. The output voltage is ofthe form:

    V.sub.o =K θNcosNt+K ψN sinsin Nt                (2)

where K is a sensitivity constant for the bender element, θ representsthe angular displacement or tilt of the spin axis in the Y-Z plane, andψ represents the angular displacement or tilt of the spin axis in theX-Z plane. θ and ψ are, respectively, dθ/dt and dψ/dt or angular rates,respectively, about the Y-axis and the X-axis as shown in FIG. 1. In theutilizing circuits, the output voltage V_(o) is phase detected andmeasured to determine the desired rates θ and ψ. V_(o) is an inherentlybias-free AC signal; signal-to-noise ratios of several dB are exhibitedat input rates equivalent to earth rate or less.

FIG. 5 illustrates an elementary form of a two-axis linear accelerometersuch as the PE crystal assemblies 50, 52 of FIG. 1. Anacceleration-sensitive device 90 such as a piezoelectric bender elementhaving an axis of sensitivity along a line 91 is affixed to a rotatingelement or shaft 92 rotating at an angular velocity ω_(n) about a spinaxis 93. Acceleration components anywhere in the plane perpendicular tothe spin axis 93 (the plane of the paper in FIG. 5) are measured; sincesuch a plane is defined by two axes, the illustrated sensor is referredto as a two-axis accelerometer. Assuming that FIG. 5 shows theacceleration-sensitive element 90 at a reference time ω_(n) t=0; that aforce on the positive (+) side of the element 90 generates a positivevoltage proportional to the force; and that the force is localacceleration a(t) acting on the mass of the acceleration-sensitivedevice 90, then because of the rotation, the voltage generated is of theform:

    v.sub.1 =K a(t) sin (∫.sub.n t+α)               (3)

where K is a scale factor, a(t) is the local acceleration, α is an anglebetween a reference axis 94 of the acceleration-sensitive device 90 andthe acceleration force a(t), the latter represented by a line 95. Autilizing means would typically measure the amplitude and phase of thevoltage generated by the acceleration-sensitive device 90 to determinethe amplitude and direction of the acceleration a(t); however, a problemarises when the measured acceleration contains a component at afrequency 2ω_(n) as well as the normally steady-state or low frequencyacceleration (g) which is the quantity of interest to be measured. Thatis, if

    a(t)=g+a.sub.1 sin 2ω.sub.n t                        (4)

the voltage generated with reference to equation (3) contains a termwhich renders g indistinguishable from the 2ω_(n) accelerationcomponents. The problem is pervasive since rotating elements such as therotating element 92 characteristically comprise ball bearings whichcommonly generate a 2ω_(n) acceleration component.

The scale factor of the acceleration sensor is not determined by thespin speed of the sensor assembly since no coriolis is involved, thecoriolis term being perpendicular to the sensitive axis of theacceleration sensor. Assuming that a constant acceleration (such asgravity) component exists along the line 91, the acceleration sensor 90is bent by its own weight, and the bending direction is the samedirection as the shaft 92 rotation. After the shaft 92 rotates 180°, thebending moment is essentially equal and opposite; therefore, asinusoidal output signal is generated, the amplitude and phase dependingon the relative direction of the g field in the sensitive plane. Theaccelerometer sensitivity has the form: ##EQU1## Note that n is not ascale factor, and that (χ₂ -χ₁) is the length of the active sensor. Ifthe acceleration a_(xy) (t) is a sinusoidal vibration ω_(a), the chargeoutput has a sinusoidal component at frequencies (ω_(a) +N) and (ω_(a)-N). For most frequencies, these terms do not result in steady-stateoutputs., however, certain harmonic frequencies such as ω_(a) =2n causepotentially serious performance problems. At ω_(a) =2n a 1n signal and a3n signal are generated. The 3n signal is rejected, but the 1n signalhas the appearance of steady-state acceleration.

In order to measure the nominally steady-state component g in thepresence of a 2ω_(n) term, a second acceleration-sensitive device 96 ismounted to the rotating structure 92 and oriented at 90° from the firstdevice 90 as shown in FIG. 5. The devices 90, 96 may be angularlydisplaced from each other by any non-zero angle, however, a 90° offsetis preferred. If the sensitivity of the devices 90, 96 are virtuallyidentical and the devices 90, 96 are physically oriented 90° apart, the2ω_(n) component will be cancelled if the output signal from the secondacceleration-sensitive device 96 is shifted in phase by 90° and added tothe output signal from the first device. Assume that a local gravityfield g exerts a force along the null axis 94 of the sensor 90 at ωt=0,and that a positive force on the + side of the sensors 90, 96 generates,respectively, positive voltages v₁ and v₂. Because the rotating element92 rotates at an angular ve1ocity ω.sub. n, the sensor assembly acts asa modulator, and

    v.sub.out =K a(t) sin ω.sub.n t                      (6)

Let

    a(t)=g+H sin (2ω.sub.n t +β)                    (7)

Then

    v.sub.1 =[g sin ω.sub.n t+H sin (2ω.sub.n t+β sin ω.sub.n t] K.sub.1                                  (8)

    v.sub.2 =[g cos ω.sub.n t+H sin (2ω.sub.n t+β) cos ω.sub.n t] K.sub.2                                  (9)

Using the identities

    sin α sin β=1/2 cos (α-β)-1/2 cos (α+β) (10)

    sin α cos β=1/2 sin (α+β)+1/2 sin (α+β) (11)

Then

    v.sub.1 =[g sin ω.sub.n t+H/2 cos (ω.sub.n t+β)-H/2 cos (3ω.sub.n t+β)]K.sub.1                         (12)

    v.sub.2 =[g cos ω.sub.n t+H/2 sin (ω.sub.n t+β)+H/2 sin (3ω.sub.n t+β)]K.sub.2                         (13)

With only one sensor 90 or 96, H corrupts the apparent applitude andphase of the acceleration vector g, and a 3ω_(n) signal is generated andmust be rejected. Ignoring in this instance the 3ω_(n) component,cancellation of the H terms is accomplished if v₂ is delayed 90°electrically, whereby v₂ delayed becomes v₂₂ and

    v.sub.22 =[g sin ω.sub.n -H/2 cos (ω.sub.n t+β)] K.sub.22 (14)

    v.sub.1 =[g sin ω.sub.n t+H/2 cos (ω.sub.n t+β)] K.sub.1 ( 15)

adding (14) and (15) cancels the H terms if the scale factors K₁ and K₂₂associated with the sensors 90, 96 are identical.

Referring again to FIG. 1, undesirable accelerations occurring in thespin plane (X,Y) of the sensor assmbly 10 which may be caused bymechanical misalignments in the sensor assembly 10 and/or externallyapplied vibrations, apply force along the length of the rate sensors 36,38. If the electrical null axis of the sensors 36, 38 is exactly in theX,Y plane, no output signal resulting from the unwanted accelerations isgenerated; however, such exactness is achieved only through precisionmechanical assembly which precludes low-cost implementation. The presentinvention achieves low-cost implementation by providing electronic meansfor compensating for imprecise mechanical construction. Referring now toFIG. 6A, there is shown a simplified diagram of a pair of piezoelectricbender elements 100, 102 mounted on a rotating member 104 having a spinaxis along a line 105. The spin axis 105 is parallel with coriolisacceleration components to be measured by the bender elements 100, 102,the coriolis accelerations being developed when the spin axis 105 isrotated in space. The resulting acceleration is proportional to the rateof rotation of the rotating member 104 and is a well-known phenomenon.Referring now to the bender element 100 of FIG. 6A (the description,however, being applicable to either element 100, 102), the benderelement 100 is mounted on the rotating member 104 such that anacceleration sensitive axis 106 of the sensor 100 is essentiallyparallel with the spin axis 105, i.e., as parallel as mechanicalconstruction will allow, but shown considerably offset in the drawingfor illustrative purposes. A null axis 107 of the sensor 100 exists suchthat steady-state or low frequency (relative to the resonant frequencyof the sensor 100) accelerations along the null axis 107 generate nooutput signals from the sensor 100. On the other hand, accelerationcomponents along the acceleration-sensitive axis 106 result in thegeneration of an electrical signal V_(c) in the sensor 100 which is ofthe form:

    V.sub.c =Kφω.sub.n sin (ω.sub.n t+α) (16)

When the sensor 100 is misaligned by an angle δ₁, from a true null axis107¹ of the assembly as shown in FIG. 6A and/or by an angle δ₂ from atrue null axis 107¹¹ as shown in FIG. 6B, and if a cross-axisacceleration 108 exists, then the sensor 100 generates a signal V_(ca)responsive to the cross-axis acceleration 108 which is of the form:

    V.sub.ca =K aδ sin (ω.sub.n t+α)         (17)

where α is a phase shift dependent on the orientation of themisalignment. Under certain circumstances, the signal output resultingfrom the misalignments δ₁ and δ₂ are indistinguishable from the desiredsignal. Misalignments δ₁ and δ₂ can be eliminated or reduced totolerable levels by precise mechanical construction; however suchprecision construction is costly. Referring now to FIGS. 6A-C, FIG. 6Cis a simplified vector diagram representative of the output signalsdeveloped by a misaligned acceleration-sensitive components such as thesensor 100. The existence of misalignments δ₁ and δ₂ results in aninterfering signal represented by the vector 110. An interfering signalsuch as the signal 110 can be expected to be of random phase fornon-precision assembly, i.e., the signal 110 may fall in any quadrant ofthe FIG. 6C diagram. Means must therefore be provided which compensatefor an interfering signal at any angle. Cross-axis accelerationcompensation is accomplished in accordance with the present invention bytwo additional acceleromters 112, 114 mounted on the rotating member104. The accelerometers 112, 114 measure the accelerations in the entireplane 116 perpendicular to the spin axis 105. While the accelerometers112, 114 are shown angularly displaced from each other by 90°, they canbe mounted at any non-zero angle with respect to each other; however, anominal 90° separation is the preferred alignment. Referring still toFIGS. 6A-C, it is assumed that the accelerometers 112, 114 are alignedsuch that they nominally generate signals represented by vectors 118 and119. Opposing vectors 120 and 121 may be generated by inverting,respectively, signals representative of the vectors 118 and 119; sincethe offending vector 110 can fall in any quadrant, a cancelling vector110¹ must be configurable for any quadrant. A cancelling vector can begenerated in any quadrant by effecting the sums of selected ones of thefour vectors 118, 119, 120, 121 of sufficient amplitude to form thedesired vector. In the example illustrated in FIG. 6C, the cancellingvector 110¹ is generated by selecting proper amplitudes of the 3π/2vector 119 and the π vector 120. Referring now to FIG. 6D, theacceleration-sensitive devices 100, 102, 112, 114 described withreference to FIGS. 6A and 6B, are represented in FIG. 6D as sine wavegenerators 100, 102, 112, 114. The output signals of the rate sensors100, 102 are combined after amplification in amplifiers havingrespective gains K5 and K6 in a summing means 122, the output signal ofthe summing means 122 comprising a desired signal 123 representative ofthe sensed angular rates plus the interfering signal 110. The outputsignals of the acceleration sensors 112, 114 are utilized to form thecancelling vector 110¹ by adjusting the appropriate gains Kl, K2corresponding respectively with the positive and negative output signalvectors 118, 120 of acceleration sensor 112, and gains K3, K4corresponding respectively with the positive and negative output signalvectors 119, 121 of acceleration sensor 114, and selectively applyingthese signals to a summing means 124 along with the summed outputsignals of the angular rate sensors 100, 102. In the summing means 124,the cancelling vector 110¹ compensates for the interfering vector 110,and the output signal 123 consequently comprises only the desiredangular rate components.

FIG. 4 is a simplified block diagram of a two-axis rate and accelerationsensor assembly such as the sensor assembly 10 of FIG. 1, and thecircuits associated therewith. THe sensor assembly comprises a spinmotor having a fixed stator assembly represented by the block 140 and arotating assembly 141; circuits carried on the rotating assembly 141 aremounted on annular printed circuit boards previously described withreference to FIG. 1. The spin motor is a hysteresis synchronous motordriven by an inverter 142 operating from a regulated DC power source143. A power inverter 144 serves as an AC power source for the circuitson the rotating assembly 141, the AC being coupled via an air-gaptransformer 145 to a power supply 146 on the rotating assembly 141. Thepower supply 146 rectifies and filters the AC and supplies DC operatingvoltage to the circuits carried on the rotating assembly 141. Timingcircuits 148 generate control signals and timing pulses forsynchronizing and controlling the operation of the sensor circuits. Thetiming circuits 148 receive an input derived from a precision clocksource, such as a 640 kHz crystal oscillator 149 shown in the presentlydescribed embodiment. A synchronizing signal representative of theposition of the rotating assembly 141 with respect to the fixed elementsof sensor assembly is coupled from a transducer 150 via a sync pulsedetector 151 to the timing circuits 148. The source of the synchronizingsignal may be a magnetic element 152 affixed to the rotating assembly towhich the transducer 150, e.g. a variable-reluctance coil, is responsiveas the magnetic element 152 passes the fixed element 150. The positionreference of the rotating assembly 141 may be generated alternatively byany suitable means such as optoelectronic devices.

Four miniature piezoelectric bender elements 154, 155, 156, 157 mountedon the rotating assembly 141 are used to sense the acceleratons ofinterest. Two sensors 154, 155 are oriented with their sensitive axesparallel to the spin axis (as previously shown with reference to FIG. 1)to measure coriolis acceleration proportional to rates of turn aboutselected axes perpendicular to the spin axis. Two other sensors 156, 157are mounted with their sensitive axes perpendicular to the spin axis formeasuring linear accelerations in the plane perpendicular to the spinaxis. Sinusoidal electrical signals generated by the rate sensors 154,155 are coupled, respectively, via buffer amplifiers 160, 161 to asumming amplifier 162. Output signals generated by the accelerationsensor 156 are coupled via a buffer amplifier 164 and a 90° phase shiftcircuit 165 to a summing amplifier 166; output signals generated by theacceleration sensor 157 are coupled via a buffer amplifier 167 to thesumming amplifier 166. A rate G-sense nulling circuit 170 provides meansfor coupling selectable portions of the signals generated by theacceleration sensors 156, 157 to the summing amplifier 162 forcancelling undesired signals representative of cross-axis accelerationssensed by the rate sensors 154, 155. The output signals of the summingamplifiers 162, 166 drive, respectively, two linear voltage-to-frequencyconverters 172, 173 which generate a frequency-modulated pulse train andserve to transmit the FM signals off the rotating assembly 141 viaair-core transformers 174, 175. The frequency-modulated pulses areconverted back to analog voltages in frequency-to-voltage converters176, 177. The regenerated signals output from the frequency-to-voltageconverters 176, 177 are sinusoidal at the spin frequency of the rotatingassembly 141, having amplitude and phase representative of therespective rate and acceleration components sensed by the rotatingcrystal assemblies. Sin/Cos demodulators 180, 181 regenerate the analogvoltages representative, respectively, of angular rate about two axes,and linear acceleration along two axes. Timing signals from the timingcircuits 148 control the regeneration of the analog voltages; thesynchronizing signal from the sync pulse detector 151 allows adjustmentof the phase of the demodulator sampling function to compensate forphase shifts in the system. The demodulator 180, 181 output signals arefiltered to remove the carrier (spin frequency) harmonics, and arecoupled to an external user device such as an aircraft attitude andheading reference system via buffer amplifiers 186, 187, 188, 189.

Referring now to FIG. 7, a detailed electrical schematic diagram of therotating assembly 141 of FIG. 4 is shown. Reference characters of likecircuit elements are the same in FIGS. 4 and 7. The circuits depicted inFIG. 7 are divided generally into two groups; the circuits shown in theupper portion of FIG. 7 (the longer dimension being orientedhorizontally) and designated generally by reference character 54' arerate sensing circuits, the components of which are carried on theannular printed circuit board 54 shown in FIGS. 1 and 2. The circuitsdepicted in the lower portion of FIG. 7 and designated generally byreference character 56' are acceleration circuits, the components ofwhich are carried on the annular printed circuit board 56 shown in FIGS.1 and 2. The bender elements 154, 155, 156, 157 of FIG. 6 correspondwith the crystal assemblies 36, 38, 50, 52 of FIG. 1. The rate sensingpiezoelectric bender elements 154, 155 are connected, respectively, tonon-inverting inputs of the buffer amplifiers 160, 161. The rate sensors154, 155 are mounted diametrically opposed on the rotating assembly 141,and therefore are electrically connected to the respective amplifiers160, 161 in opposite electrical polarity with respect to each other asindicated by the literal designations A and B adjacent to each sensor154, 155 in FIG. 7, such that respective output signals at junctionpoints 190, 192 are in phase or additive. A balance potentiometer 194 isutilized during manufacture of the sensor assembly to compensate for anydifferences in the amplitude of the output signals at terminal points190, 192; such differences in signal amplitude may be caused by slightlydifferent circuit gains in the amplifiers 160, 161 or by imperfect,i.e., unmatched construction of the piezoelectric crystal assemblies154, 155.

The acceleration-sensing piezoelectric bender elements 156, 157 areconnected, respectively, to non-inverting inputs of the bufferamplifiers 164, 167. The output signal of the buffer amplifier 164 atjunction point 200 is coupled to the 90° phase shift circuit 165. Thesignal output of the phase shift circuit 165 at junction point 202 iscoupled via a balance potentiometer 204 to the input of the summingamplifier 166 at junction point 206. The output signal of the bufferamplifier 167 at junction point 208 is coupled via the balancepotentiometer 204 to the input 206 of the summing amplifier 166. Thepiezoelectric bender elements 156, 157 are mounted on the rotatingassembly 141 angularly displaced from each other 90°; the circuit 165shifts the phase of the signal generated by the bender element 156 by90° so that the respective signals at the junction points 202, 208 arein phase and additive when applied to the input 206 of the summingamplifier 166. Undesirable acceleration components sensed by theacceleration sensors 156, 157 are thereby cancelled in the summingamplifier 166 as previously described with reference to FIG. 5.

Cross-axis accelerations sensed by the rate sensors 154, 155 arecompensated for during manufacture of the sensor assembly by signalselection and adjustment in the nulling circuits 170. A portion of thesignal at junction point 200 representative of the acceleration sensedby the piezoelectric bender element 156 is coupled via an interboardjumper 212 to one of the input junction points 196, 214 of the summingamplifier 162, the amplitude of the signal being selected by adjustmentof a potentiometer 216 and the direction or polarity of the vector beingselected by installing an appropriate one of a pair of jumper wires orstraps 218. Similarly, a portion of the output signal at junction point208 representative of linear acceleration sensed by the piezoelectricbender element 157 is coupled via another interboard jumper wire 212 toone or the other of the input junction points 196, 214 of the summingamplifier 162, the amplitude of the coupled signal being selected byadjustment of a potentiometer 220, and the signal polarity beingselected by installation of an appropriate one of the jumper wires 218to connect the coupled signal either to the inverting 196 or thenon-inverting 214 input of the summing amplifier 162. The output signalof the summing amplifier 162 at junction point 222 consequently isrepresentative only of the desired angular-rates sensed by thepiezoelectric bender elements 154, 155, the cross-axis accelerationcomponents having been nulled out by compensating signals formed in thenulling circuits 170.

The rate signals at the junction points 222 are coupled through alinearizing circuit 224 to the voltage-to-frequency converter 172. Theoutput signal of the voltage-to-frequency converter 172 comprises aseries of pulses 4 microseconds wide having a center frequency ofapproximately 60 kHz which varies in frequency proportional to theapplied input voltage. The frequency-modulated output pulse train iscoupled to the transformer 174 for transmission off the rotating element141. The linearizing circuit 224 utilizes feedback from thevoltage-to-frequency converter 172 to a node at input junction point225. The linearizing circuit 224 serves to improve the linearity of therate signal, the rate signal having an inherently low level comparedwith the acceleration signal in the prevailing operating environment,i.e., during straight and level flight, when the vehicle experiences arelatively constant one-g acceleration field and comparatively very lowrate-signal perturbation. The output signal of the summing amplifier 166at junction point 210 is coupled to the voltage-to-frequency converter173. The output signal of the voltage-to-frequency converter 173 is aseries of pulses four microseconds wide having a center frequency offsetapproximately 2 kHz from the center frequency of thevoltage-to-frequency converter 172, which center frequency varies inproportion to the applied input voltage. The output signal of thevoltage-to-frequency converter 173 is coupled to the transformer 175 fortransmission off the rotating assembly 141. The center frequencies ofthe voltage-to-frequency converters 172, 173 are offset to precludecross-coupling of the acceleration signals to the rate signal circuits54' when the aircraft is in straight and level flight and the ratecircuits exhibit virtually zero signal output.

The circuits of FIG. 7 utilize commercially available integrated circuitcomponents. The summing amplifiers 160, 161, 164, 167 are LM108Aoperational amplifiers; the summing amplifiers 162, 166, the phase shiftcircuit 165 and the linearizing circuit 224 are LM1558 operationalamplifiers; the voltage-to-frequency converters 172, 173 are LM131Aintegrated circuits; all are manufactured by National SemiconductorCorporation. The power supply 146 on the rotating assembly 141 comprisesa full wave rectifier utilizing 1N4454 diodes, a positive regulator 226and a negative regulator 227. The regulators 226, 227 of thepresently-described embodiment are, respectively, μA78M05 and LM120integrated circuit modules manufactured, respectively, by FairchildCamera and Instrument Corporation and National SemiconductorCorporation. Unregulated DC is supplied via interboard jumper wires 228to another set of regulators (not shown) on the acceleration circuitboard 56.

While the principles of the invention have been made clear in anillustrative embodiment, there will be immediately obvious to thoseskilled in the art many modifications of structure, arrangement,proportions, the elements, material and components that may be used inthe practice of the invention which are particularly adapted forspecific environments without departing from those principles. Theappended claims are intended to cover and embrace any such modificationswithin the scopes only of the true spirit and scope of the invention.

What is claimed is:
 1. A sensor assembly, comprising:an inside-out motorhaving a central shaft fixed with respect to a major axis of referenceof a vehicle, a stator affixed to the shaft, and a rotating elementincluding a motor housing, means for journaling the motor housing to theshaft, the motor housing having a spin axis coaxial with the shaft, andcylindrical means mounted inside the motor housing and juxtaposed withthe stator for driving the motor housing, the motor housing being drivenat a substantially constant spin frequency in response to alternatingcurrent applied to the stator; a first cantilevered piezoelectric benderelement mounted exteriorly on the motor housing for rotation therewith,said first bender element having a bending axis essentially normal tothe spin axis of the cylindrical housing and an axis of sensitivityessentially parallel with the spin axis of the motor housing; second andthird cantilevered piezoelectric bender elements mounted exteriorly onthe motor housing for rotation therewith, said second and third benderelements each having a bending axis essentially parallel with the spinaxis of the motor housing and an axis of sensitivity essentially normalto the spin axis of the motor housing, the axes of sensitivity of saidsecond and said third bender elements being angularly displaced fromeach other; a circuit-bearing substrate mounted exteriorly on the motorhousing for rotation therewith; first circuit means on saidcircuit-bearing substrate responsive to an electrical signal generatedby said first bender element for generating a first output signalrepresentative of angular displacement with respect to inertial space ofthe major axis of reference of said vehicle; second and third circuitmeans on said circuit-bearing substrate each responsive to an electricalsignal generated, respectively, by said second and said third benderelements for generating, respectively, a second and a third outputsignal representative of linear acceleration of said vehicle in a planeperpendicular to the major axis of reference of said vehicle, theinstantaneous direction of the linear acceleration sensed being alongthe axes of sensitivity of said second and said third bender elements;means coupled to said first circuit means for selecting a portion ofeach said second and said third output signals, said first circuit meansincluding means for summing said signal portions with the first outputsignal to cancel signal components representative of cross-axisaccelerations sensed by said first bender element.
 2. The sensorassembly as claimed in claim 1, wherein said first circuit means furthercomprises circuit means for linearizing the first output signal.
 3. Asensor assembly, comprising:a rotating member having an axis of rotationfixed with respect to an axis of reference of a vehicle, said rotatingmember having a substantially constant frequency of rotation; a firstpiezoelectric bender element mounted on said rotating member forrotation therewith, said first bender element having a bending axisessentially normal to the axis of rotation and an axis of sensitivityessentially parallel with the axis of rotation; first circuit meansmounted on said rotating member and responsive to an electrical signalgenerated by said first bender element for generating a first outputsignal at the frequency of rotation representative of angulardisplacement with respect to inertial space of the vehicle, theelectrical signal generated by said first bender element and the firstoutput signal including an interfering signal component representativeof cross-axis acceleration sensed by said first bender element due tomechanical misalignment of said first bender element; a secondpiezoelectric bender element mounted on said rotating member forrotation therewith, said second bender element having a bending axisessentially parallel with the axis of rotation and an axis ofsensitivity essentially perpendicular to the axis of rotation; secondcircuit means mounted on said rotating member and responsive to anelectrical signal generated by said second bender element for generatinga second output signal at the frequency of rotation representative oflinear acceleration of the vehicle in a plane normal to the axis ofrotation; a third piezoelectric bender element mounted on said rotatingmember for rotation therewith, said third bender element having abending axis essentially parallel with the axis of rotation and an axisof sensitivity essentially perpendicular to the axis of rotation, theaxis of sensitivity of said third piezoelectric bender element beingangularly offset from the axis of sensitivity of said secondpiezoelectric bender element; third circuit means mounted on saidrotating member and responsive to an electrical signal generated by saidthird bender element for generating a third output signal at thefrequency of rotation representative of linear acceleration of thevehicle in a plane perpendicular to the axis of rotation; meansreceiving the first output signal for summing electrical signals; meansselectively coupling portions of the second and the third output signalsto said summing means for cancelling the interfering signal component.4. A sensor assembly, comprising:a rotating member supported on avehicle and having an axis of rotation fixed with respect to an axis ofreference of the vehicle; a first cantilevered piezoelectric benderelement mounted on said rotating member for rotation therewith, saidfirst bender element generating a first electrical signal at thefrequency of rotation of said rotating member and representative of rateof rotation of the vehicle about an axis perpendicular to the axis ofrotation, the first electrical signal having an undesired signalcomponent representative of linear acceleration of the vehicle in aplane perpendicular to the axis of rotation sensed by said first benderelement as a result of mechanical misalignment of said first benderelement with respect to a null axis of said first bender element; firstcircuit means mounted on said rotating member and coupled to said firstbender element for amplifying said first electrical signal; a secondcantilevered piezoelectric bender element mounted on said rotatingmember for rotation therewith, said second bender element generating asecond electrical signal at the frequency of rotation of said rotatingmember and representative of linear acceleration of the vehicle in aplane perpendicular to the axis of rotation, said second bender elementhaving an axis of sensitivity in the perpendicular plane; second circuitmeans mounted on said rotating member and coupled to said second benderelement for amplifying the second electrical signal; a thirdcantilevered piezoelectric bender element mounted on said rotatingmember for rotation therewith, said third bender element generating athird electrical signal at the frequency of rotation of said rotatingmember and representative of linear acceleration of the vehicle in aplane normal to the axis of rotation, said third bender element havingan axis of sensitivity in the normal plane, the axis of sensitivity ofsaid second and said third bender elements being angularly displacedfrom each other; third circuit means mounted on said rotating member andcoupled to said third bender element for amplifying the third electricalsignal; fourth circuit means mounted on said rotating member coupled tosaid first circuit means and receiving as one input thereto theamplified first electrical signal for summing electrical signals; fifthcircuit means mounted on said rotating member and coupled to said fourthcircuit summing means and to said second and said third circuit meansfor selectively applying a portion having predetermined amplitude andpolarity each of the second and the third electrical signals as secondand third input signals to said fourth circuit summing means, the secondand the third input signals nulling the undesired component of the firstelectrical signal in said fourth circuit summing means; and sixthcircuit means for coupling an output signal of said fourth circuitsumming means off said rotating member to a utilization means, theoutput signal being representative of rate of rotation of the vehicleabout the axis perpendicular to the axis of rotation.
 5. The sensorassembly as claimed in claim 4, wherein said sixth circuit meansincludes circuit means for linearizing the output signal.
 6. A sensorassembly for measuring the angular rate of rotation of a vehicle withrespect to inertial space, comprising:a rotating member supported on thevehicle and having an axis of rotation fixed with respect to thevehicle, said rotating member being driven at a substantially constantfrequency of rotation, said rotating member including a firstcantilevered piezoelectric bender element having orthogonal null axesessentially perpendicular to the axis of rotation, said first benderelement generating a first sinusoidal electrical signal at the frequencyof rotation in response to coriolis forces exerted on said benderelement in a direction essentially parallel with the axis of rotationdue to rotation with reference to inertial space of the vehicle, thefirst electrical signal being representative of the angular rate ofrotation of the vehicle, which first electrical signal may include aninterfering signal component representative of cross-axis accelerationdue to misalignment of the null axis, said rotating member including asecond and a third piezoelectric bender element, each having an axis ofsensitivity essentially perpendicular to the axis of rotation andangularly displaced from each other, each of said second and said thirdbender elements generating a sinusoidal electrical signal at thefrequency of rotation representative of linear acceleration in a planeperpendicular to the axis of rotation, each of the second and the thirdelectrical signals having a phased relationship to the othercorresponding with the displacement angle, said rotating memberincluding circuit means for selecting portions of the second and thethird electrical signals, each of the signal portions having anamplitude and a polarity which when combined will form a signal vectorequal and opposite to the interfering signal component, and saidrotating member including circuit means for summing the first, thesecond, and the third electrical signals to cancel the interferingsignal component.